Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A proof that $ \mathcal{C}^2$ and $ \mathcal{T}^2$ are distinct measures


Author: Lawrence R. Ernst
Journal: Trans. Amer. Math. Soc. 173 (1972), 501-508
MSC: Primary 28A10
MathSciNet review: 0310164
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that there exists a nonempty family $ X$ of subsets of $ {{\text{R}}^3}$ such that the two-dimensional Carathéodory measure of each member of $ X$ is less than its two-dimensional $ \mathcal{T}$ measure. Every member of $ X$ is the Cartesian product of 3 copies of a suitable Cantor type subset of $ {\text{R}}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28A10

Retrieve articles in all journals with MSC: 28A10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0310164-3
PII: S 0002-9947(1972)0310164-3
Keywords: $ m$-dimensional measures, two-dimensional Carathéodory measure, two-dimensional $ \mathcal{T}$ measure, Cantor type subsets, Steiner symmetrization
Article copyright: © Copyright 1972 American Mathematical Society